If the mask patterns are implemented using a pixelated spatial light modulator, specifying their design to be orthogonal is straightforward (e.g. Hadamard, or similar). If, however, the patterns are produced in other ways, e.g. using natural scattering or with the highly limited modulators available in a TEM, then orthogonality between the patterns can no longer be enforced and the standard reconstruction algorithms no longer converge to an accurate image. The TGI algorithm in particular will overemphasise the overlapping parts of the patterns. To resolve this issue, we report an alternative approach that is computationally efficient and makes optimal use of patterns regardless of their orthogonality. This alternative method, which we will call orthogonalised ghost imaging (OGI), takes inspiration from the Kaczmarz algorithm for solving linear systems [1]}, [2]}, [3]}, [4]}, [5]}.
